Creep Function of a Single Living Cell

Abstract

We used a novel uniaxial stretching rheometer to measure the creep function J(t) of an isolated living cell. We show, for the first time at the scale of the whole cell, that J(t) behaves as a power-law J(t) = At(alpha). For N = 43 mice myoblasts (C2-7), we find alpha = 0.24 +/- 0.01 and A = (2.4 +/- 0.3) 10(-3) Pa(-1) s(-alpha). Using Laplace Transforms, we compare A and alpha to the parameters G(0) and beta of the complex modulus G*(omega) = G(0)omega(beta) measured by other authors using magnetic twisting cytometry and atomic force microscopy. Excellent agreement between A and G(0) on the one hand, and between alpha and beta on the other hand, indicated that the power-law is an intrinsic feature of cell mechanics and not the signature of a particular technique. Moreover, the agreement between measurements at very different size scales, going from a few tens of nanometers to the scale of the whole cell, suggests that self-similarity could be a central feature of cell mechanical structure. Finally, we show that the power-law behavior could explain previous results first interpreted as instantaneous elasticity. Thus, we think that the living cell must definitely be thought of as a material with a large and continuous distribution of relaxation time constants which cannot be described by models with a finite number of springs and dash-pots.

Slow dynamics, aging, and glassy rheology in soft and living matter

“…Similar glassy behaviour is also observed in the rat airway smooth muscle during actin modulation [72]. The scale-free soft glassy rheology of living cells has been a subject of recent research [73,74,75].…”

Multiple‐Particle Tracking and Two‐Point Microrheology in Cells

“…In the active approach, a known force (or deformation) is applied to the material, and the resulting deformation (or force) is measured. In the cell rheology context, this usually relies upon atomic force microscope (AFM) (Alcaraz, 2003) or similar, force calibrated micro-cantilever instruments (Desprat, 2005). The passive approach, which is our focus in this chapter, examines the Brownian motion of tracers embedded in the soft material.…”

“…In reality, however, the rheological responses of cells measured to date have not contained identifiable molecular timescales and have not been satisfactorily reproduced by any biopolymer gel model yet studied. Several recent experiments have found the (low frequency) shear modulus of cells to be well described by a weak power-law form, G*(ω)~ω β , with reported values of β varying over the range 0.1-0.3 (Yamada, 2000;Fabry, 2001;Alcaraz, 2003;Lenormand, 2004;Desprat, 2005;. Such a power-law form has no characteristic times at all.…”

Direct observation of dynamic force propagation between focal adhesions of cells on microposts by atomic force microscopy

“…24 Figure 2(b) is a plot of jE*j normalized by that at f ¼ 0.01 Hz as a function of f. It is clearly seen that the relative value of jE*j follows a single power law, which has been commonly measured at local regions of single cells 25 and in a whole single cell that was largely deformed during stretching. 26 In the present experiments, cell deformation was ca. 4.5 lm, which was between the former and latter experimental conditions, in which cells suffered no fatal damage during force application.…”